Rising birth rate

But the next big increase will be in secondary schools, currently with 2.76 million pupils and forecast to rise to 3.04 million in 2020 and then 3.33 million in 2025.

It means that within the next decade secondary schools will have to create an extra 570,000 places - and these figures do not include post-16 education or sixth forms.

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The biggest increases are going to be in the secondary age group, up by 570,000 in a decade

The increase has been driven by a rising birth rate - and the analysis says this reflects an increasing number of non-UK born mothers, who tend to have bigger families.

The forecast says "direct immigration of pupils" has had only a very small effect.

Russell Hobby, leader of the National Association of Head Teachers, said there needed to be much better integrated planning for extra places, including the involvement of local authorities.

"We are looking at over 750,000 more young people in school education by 2025. The government's only clear plan for increasing capacity is to open 500 free schools. Whilst good, new free schools are fine, they are not sufficient.

"The government will also need to take teacher recruitment and retention more seriously," said Mr Hobby.

The New Schools Network, which supports the opening of free schools, says that when all the free schools that are open and which have been approved are at full capacity they will have created an extra 250,000 places.

Sarah Pearson, interim director, said: "We mustn't lose sight that they are also about bringing new people and ideas into education and driving up standards across the board."

Teacher shortage

There have been warnings from school leaders about a shortage of teachers and problems with retention - and figures from the Institute for Fiscal Studies, published on Friday, showed that 40% of teachers who enter initial teacher training were not teaching five years later.

It means that 14,000 people who enter teacher training each year are not in the classroom five years later.

A Department for Education spokeswoman said the government had already committed £7bn to the "top priority" of creating school places, which along with more free schools, would provide 600,000 more places in the next five years.

"The latest figures show that the system is responding well to growing numbers of pupils - fewer children are being taught in large infant classes, the average primary school class sizes remain stable at 27.1 pupils and the vast majority of parents get places in their preferred schools."